Question concerning Bernoulli's demonstration of Bernoulli's Weak Law of Large Numbers.
Although, I get the general sense of the third lemma, I don't really get the formulation of it, more particularly the use of the word "ratio":
"Lemma 3: In any expansion of the binomial (r+s) raised to a power which is the multiple of the binomial - that is, raised to a power t where t = nr + rs, n a natural number - if some terms precede and other terms follow a certain term M such that the number of all those preceding is in the ratio to the number of all those following as s is to r, (or if restating this, the exponents of the r and of the term s in M are in the ratio r : s), then this term M will be the largest one in the expansion, and the closer a term is to M, the larger is its value. Moreover, the ratio between this term M and another term V a given distance from M is smaller than the ratio between V and another term W the same distance away from V"
I cited the second lemma entirely, the text can be found at (page 15) : http://cerebro.xu.edu/math/Sources/JakobBernoulli/ars_sung.pdf
Could someone help me with that?